A New Method for Discretization of Continuous-time Systems Using the Pade Approximation Applied to IIR Filters

The paper presents an effective procedure for the discretization of linear continuous-time systems applied to Infinite Impulse Response (IIR) filters. Unlike conventional techniques which use some established rational s-to-z mapping functions (such as Tustin approximation etc.), in the proposed two-staged discretization method, the fundamental, non-rational mapping of the continuous to discrete domain s=ln(z)/T (with adequate sampling time $T$), is substituted to the IIR filter transfer function. The Pade approximation is then directly applied to the obtained overall non-rational discrete-time transfer function. Besides, the Pade approximation may be applied partially to factored parts of the transfer function, also including a combination of the proposed with existing classical discretization schemes. As a result, amplitude and phase-frequency characteristics of the digital model are preserved with high accuracy in a wide frequency range relative to the original continuous-time system. The presented approach is compared with conventional discretization schemes (Tustin approximation, step-invariant discretization and l/sn to $z$ transform) via illustrative examples considering Butterworth, Bessel, Chebyshev Type I, and elliptic filters.